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Active‐Set Newton Methods and Partial Smoothness

Author

Listed:
  • Adrian S. Lewis

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

  • Calvin Wylie

    (School of Operations Research and Information Engineering, Cornell University, Ithaca, New York 14853)

Abstract

Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to variational inequalities over partly smooth sets. As in classical nonlinear programming, such active‐set structure underlies the design of accelerated local algorithms of Newton type. We formalize this idea in broad generality as a simple linearization scheme for two intersecting manifolds.

Suggested Citation

  • Adrian S. Lewis & Calvin Wylie, 2021. "Active‐Set Newton Methods and Partial Smoothness," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 712-725, May.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:2:p:712-725
    DOI: 10.1287/moor.2020.1075
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    References listed on IDEAS

    as
    1. A. F. Izmailov & M. V. Solodov, 2015. "Newton-Type Methods: A Broader View," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 577-620, February.
    2. Samuel Vaiter & Charles Deledalle & Jalal Fadili & Gabriel Peyré & Charles Dossal, 2017. "The degrees of freedom of partly smooth regularizers," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(4), pages 791-832, August.
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